2 Chapter 1: Polynomial Functions Function in the formType of symmetryOdd function/ even functionDegreesDomain& rangeX and y interceptFinite differenceEnd behaviourTransformation in the formLocal maximum/ minimumAverage rate of changeInstantaneous rate of change
3 Q.Find the local minimum of p(x) if End Behaviour: II quadrant to I quadrant Zeroes: x=-2 order 1, cross x=-1 order 1, cross x=2 order 2, touch and turnx-intercept: p(0)=8, (8,0)y-intercept: (0,-2) and (0,-1)Local minimum: (8,0)if
4 The volume of a balloon is given by where is the time in hour and is volume in cubic inches. Find the average rate of change between t=10 and t=13.
5 A water tank draining according to the function where t is the time in hours such that . How fast is the water draining at the end of the 3rd hour?.=-4500unit/h
6 Chapter 2: Polynomial Equations and Inequalities Remainder theorem: When a polynomial p(x) is divided by (x-a) the remainder is p(a)Factor theorem: When , (x-a) is a factor of p(x) if p(a)=0.Complex Conjugates: If (a+bi) is a root , that is (x-(a+bi)) is a factor of p(x), then (a-bi) is also a root. If is a root, then is also a root.Rational Zero theorem: If (p,q are integers s.t q does not equal to 0), then (qx-p) is a factor of the polynomial.Family of polynomial functions:Inequalities
7 The volume, V, in cubic centimetres, of a block of ice that a sculptor uses to carve the wings of a dragon can be modelled by , where x represents the thickness of the block, in centimetres. What maximum thickness of wings can be carved from a block of ice with volume 2532cm..Solve the equationUse rational theorem to list factors;Possible values;
8 Cookies are packed in boxes measure 2cm by 8cm by 10cm Cookies are packed in boxes measure 2cm by 8cm by 10cm. A larger box is designed by increasing its length, width, and height of the smaller box by same length. Find the possible dimensions of the new box if the volume Is at least ..12+2=14,12+10=22,12+8=20Possible dimensions: 6 x 12 x 14 or 14 x 20 x 22(x cannot be -12)
9 Chapter 3: Rational functions Reciprocal of Linear Functions. Review point, jump, infinite discontinuity.
10 Reciprocal of Quadratic Functions f(x)g(x)=f(x)<or>0g(x)<or>0f(a)=o,f(x) ag(x) undefinedf(x) increasingg(x) decreasingf(x)=1g(x)=1y-int of f(x) at y=by-int of g(x) at y=1/bg(x) 0If f(x) is oddg(x) is oddIf f(x) has max or min at (p,q)g(x) has max or min at (p,1/q)f(x) is eveng(x) is even